Problem: Shown below is a clock face with no hands.  What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock? [asy]
/* AMC8 1999 #2 Problem*/
draw(circle((0,0),10),linewidth(1));

/* Hands
draw((25,0)--8dir(-18)+(25,0),linewidth(2));
draw((25,0)--5dir(111)+(25,0),linewidth(2));
draw((25,0)--10dir(90)+(25,0),linewidth(.5));
*/
dot((0,0));

label("1",8dir(60));
label("2",8dir(30));
label("3",8dir(0));
label("4",8dir(-30));
label("5",8dir(-60));
label("6",8dir(-90));
label("7",8dir(-120));
label("8",8dir(-150));
label("9",8dir(180));
label("10",8dir(150));
label("11",8dir(120));
label("12",8dir(90));

for(int i = 1; i< 13; ++i)
{

draw(9dir(30i)--10dir(30i));
}
[/asy]
Solution: There are $360^\circ$(degrees) in a circle and twelve spaces on a clock. This means that each space measures $30^\circ$. At 10 o'clock the hands point to 10 and 12. They are two spaces or $\boxed{60^\circ}$ apart. [asy]
/* AMC8 1999 #2 Solution*/
draw(circle((0,0),10),linewidth(1));

/* Hands */
draw((0,0)--4dir(150),linewidth(2));
draw((0,0)--6dir(90),linewidth(2));
dot((0,0));

label("1",8dir(60));
label("2",8dir(30));
label("3",8dir(0));
label("4",8dir(-30));
label("5",8dir(-60));
label("6",8dir(-90));
label("7",8dir(-120));
label("8",8dir(-150));
label("9",8dir(180));
label("10",8dir(150));
label("11",8dir(120));
label("12",8dir(90));

for(int i = 1; i< 13; ++i)
{

draw(9dir(30i)--10dir(30i));
}
[/asy]